The mean of the following frequency distribution is $25.2$ . Find the missing frequency $x$
$C . I .$ $0 - 10$ $10 - 20$
$20 - 30$ $30 - 40$ $40 - 50$
frequency $8$ $X$ $10$ $11$ $9$

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Solution

Solution -
C.I 0-10 10-20 20-30 30-40 40-50
Frequency 8 X 10 11 9.
Midvalue 5 15 25 35 45
Mean = 25.2
$\frac{8 \times 5 + 15 x + 10 \times 25 + 11 \times 35 + 9 \times 45}{8 + x + 10 + 11 + 9} = 25.2$
$1080 + 15 x = 957.6 + 25.2 x$
$x = \frac{122.4}{10.2}$
$x = 12.$

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31.4

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Class	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$
Frequency	$5$	$x$	$10$	$12$	$7$	$8$

C.I.	0-10	10-20	20-30	30-40	40-50
Frequency	7	5	3	4	6

C.I	0-10	10-20	20-30	30-40	40-50	50-60
Frequency	12	?	27	20	17	6

f_{1}

f_{2}

N = 100

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Class	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$T o t a l$
Frequency	$10$	$f_{1}$	$25$	$30$	$f_{2}$	$10$	$100$

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10 > y > x

y =

Class interval	0-10	10-20	20-30	30-40	40-50	Total
Frequency	5	8	10	x	y	30

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$C . I .$	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$
frequency	$8$	$X$	$10$	$11$	$9$